Abstract

Covariation is recognised as an important aspect of statistical thinking and reasoning and is used to explore the relationship between two attributes. Often, covariation is determined from the interpretation of scatterplots that display the correspondence of two numerical attributes and is described as a trend in the data. Scatterplots are utilised when conducting exploratory data analysis (EDA). EDA strategies are useful for interpreting the data as they allow the data to be manipulated in order to construct graphical representations that facilitate making sense of the data. The translation of EDA strategies into innovative software packages, such as TinkerPlots: Dynamic Data Exploration, has placed student learning about data analysis in technological environments and there is a need to investigate the way in which students learn in these contexts.
This inquiry had two objectives. The first objective was to further understanding of the factors that influence student learning when working with software packages. This is through the development of a conceptual framework for learning in EDA graphing environments that aligns with and extends current research about student understanding of graphing and data analysis. The second objective was to explore the intersection between the students‘ thinking and reasoning about covariation and the influence of TinkerPlots on that process, as students explore data sets to determine the relationship between variables and identify trends. To realise these objectives the following research questions are explored:
1. How can the learning behaviours of students as they engage with exploratory data analysis software be characterised through a framework that can then be used to explore and analyse students‘ understanding of covariation using TinkerPlots?
2. How do students interact with the exploratory data analysis software, TinkerPlots, to represent data in a variety of forms when exploring questions about relationships within a data set? viii
3. How do students demonstrate an understanding of covariation in the exploratory data analysis software environment afforded by TinkerPlots and use these understandings to provide informal justification for their conclusions about the relationships identified?
The inquiry employed an educational design research methodology within a pragmatist paradigm to facilitate the development of a systematic iterative study. The methodology was chosen to encapsulate the way students learn about the interpretation of graphical representations, more specifically related to covariation, in the technological software environment afforded by TinkerPlots.
The inquiry was enacted across seven stages. Stage 0 involved the development of the research design. Stage 1 involved the development of a conceptual framework for learning in EDA software environments that incorporated four aspects of graphing and data analysis skills – Generic knowledge, Being creative with data, Understanding data, and Thinking about data. Stage 2 involved an evaluation of TinkerPlots to determine its usability as a teaching and learning tool. Stage 3 involved the development and evaluation of an assessment tool to determine the prior learning of students in relation to the interpretation of graphs, and select the participants for the data collection stage of the inquiry. Stage 4 involved the development and implementation of a sequence of learning experiences. The activities in the sequence of learning were based on recommendations from the research on the development of graphing and data analysis skills. The sequence of learning experiences was implemented with 12 students working in pairs, twice a week for 45 minutes, over a period of 6 weeks. In addition, the data generated from individual interviews with the 12 students conducted at the end of the sequence of learning were included in this stage. The data from the student interviews are presented as Student Profiles that encapsulate the way in which they used TinkerPlots to develop not only an understanding of covariation but also develop other data analysis skills and strategies. Stage 5 involved the presentation of the results for the Research Questions, with the discussion of the findings, implications of the inquiry, and recommendations for future research included in Stage 6. The presentation of the thesis follows this chronological order. Through the evaluation of TinkerPlots and its subsequent implementation in the inquiry, it was identified that TinkerPlots provides a powerful learning environment for supporting students‘ understanding of covariation. In terms of student understanding of covariation, the inquiry identified that young students are able to reason about covariation and display three levels of reasoning. The results also suggest that students adopt three different strategies when accessing the features of TinkerPlots while creating and interpreting graphs. These strategies are: Snatch and Grab, Proceed and Falter, and Explore and Complete.
Outcomes of the inquiry are presented in relation to the thesis-developed Model of Learning Behaviour in EDA Graphing Environments. Within the framework of the model the students‘ development of covariation reasoning is revealed and discussed in terms of the potential of the results to inform the teaching and learning of covariation within EDA software environments and future curriculum development. Consideration was also given to the merits of the Model of Learning Behaviour in EDA Graphing Environments and its application throughout the inquiry process. Unexpected insights into the students‘ thinking and reasoning about association are also discussed to demonstrate the utility of the thesis-developed model and to highlight the need to further research in the area of student understanding of association.